and to study its space-time regularity properties. To do so, one could use for example an Itô-Tanake trick (see [1]} in the fractional Brownian motion setting) or the corresponding Kolmogorov equation [2]}.
More recently, techniques involving stochastic sewing lemma [3]} and/or properties of the occupation measure/local time of the process [4]} where used. Once a space-time regularity of the averaged field is exhibited, one can then use some pathwise non-linear calculus [5]} to conclude. We will see in the following how this strategy of proof is implemented in our setting.
